What is the limit as x approaches 2+of (3x)/(x-2) ?

The limit as x approaches 2+of (3x)/(x-2) is infinity

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limit as x approaches 2+of (3x)/(x-2)

x \to 2 + lim (\frac{3 x}{x - 2})

\infty

Solution steps

x \to 2 + lim (\frac{3 x}{x - 2})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to 2 + lim (\frac{x}{x - 2})

Divide by highest denominator power:

\frac{1}{1 - \frac{2}{x}}

= 3 \cdot x \to 2 + lim (\frac{1}{1 - \frac{2}{x}})

For

x

approaching

2

from the right

, x > 2 \Rightarrow 1 - \frac{2}{x} > 0

The denominator is a positive quantity approaching 0 from the right

= 3 \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

\int \frac{x - 1}{x ^{2} - 3} d x

\frac{1}{5 x ^{2} + 3 x}

10 y^{^{''}} + 1000 y = 130 cos (8 t)

\frac{3}{( s - 3 ) ^{3}}

\int e^{2 x} (1 - 5 e^{2 x})^{2} d x

What is the limit as x approaches 2+of (3x)/(x-2) ?
The limit as x approaches 2+of (3x)/(x-2) is infinity